L-infinity maps and twistings

We give a construction of an $L_\infty$ map from any $L_\infty$ algebra into its truncated Chevalley-Eilenberg complex as well as its cyclic and $A_\infty$ analogues. This map fits with the inclusion into the full Chevalley-Eilenberg complex (or its respective analogues) to form a homotopy fiber sequence of $L_\infty$ algebras. Applications to deformation theory and graph homology are given. We employ the machinery of Maurer-Cartan functors in $L_\infty$ and $A_\infty$ algebras and associated twistings which should be of independent interest.

Keywords

differential graded Lie algebra, Maurer-Cartan element, $A_\infty$ algebra, graph homology, Morita equivalence

2010 Mathematics Subject Classification

16E45, 18D50, 57T30, 81T18

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Published 25 January 2012